a) \(\lim \left( {{n^2} + 2n - 5} \right)\) \( = \lim {n^2}\left( {1 + \dfrac{2}{n} - \dfrac{5}{{{n^2}}}} \right)\) \( = + \infty \).
b) \(\lim \left( { - {n^3} - 3{n^2} - 2} \right)\) \( = \lim \left[ { - {n^3}\left( {1 + \dfrac{3}{n} + \dfrac{2}{{{n^3}}}} \right)} \right] = - \infty \).
c) \(\lim \left[ {{4^n} + {{\left( { - 2} \right)}^n}} \right]\) \( = \lim {4^n}\left[ {1 + {{\left( { - \dfrac{2}{4}} \right)}^n}} \right] = + \infty \).
